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Q29
(CISF/2023)
Science & Technology › Basic Science (Physics, Chemistry, Biology)
The digit in the unit place of the number (347)192 × (143)205 is :
Explanation
To find the unit digit of the product (347)192 × (143)205, we focus on the unit digits of the individual numbers and their powers.
- For (347)192: The unit digit is 7. The cyclicity of 7 is 4 (71=7, 72=9, 73=3, 74=1). Dividing the exponent 192 by 4 gives a remainder of 0 (192 = 4 × 48). When the remainder is 0, the unit digit corresponds to 74, which is 1.
- For (143)205: The unit digit is 3. The cyclicity of 3 is also 4 (31=3, 32=9, 33=7, 34=1). Dividing the exponent 205 by 4 gives a remainder of 1 (205 = 4 × 51 + 1). Thus, the unit digit is 31, which is 3.
Multiplying the unit digits: 1 × 3 = 3. Therefore, the unit digit of the entire expression is 3.
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SIMILAR QUESTIONS
Consider the following number : n = [(6374)1793x(625)3]7x(313)49] Which one of the following is the digit at the unit place of n ?
In the sequence 462, 420, 380, X, 306. X stands for
Which one among the following digits can never be at the units place in (273)n, where n is a positive integer?